# Ex 6.1,15 - Chapter 6 Class 12 Application of Derivatives

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 6.1,15 The total cost C(𝑥) in Rupees associated with the production of 𝑥 units of an item is given by 𝐶(𝑥) = 0.007𝑥3 – 0.003𝑥2 + 15𝑥 + 4000. Find the marginal cost when 17 units are produced. Since Marginal Cost is Rate of change in total cost w.r.t No of units produced Let M C be the marginal cost & C 𝑥 is the total cost & 𝑥 be the no of units produced So, MC = 𝑑 𝑐 𝑥𝑑𝑥 It is Given that total cost C 𝑥=0.007 𝑥3−0.003 𝑥2+15𝑥+4000 & we need to find Marginal cost when 17 units produced i.e. MC at 𝑥=17 Now MC = 𝑑 𝐶 𝑥𝑥 MC = 𝑑 0.007 𝑥3−0.003 𝑥2+15𝑥+4000𝑑𝑥 MC = 𝑑 0.007 𝑥3𝑑𝑥 − 𝑑 0.003 𝑥2𝑑𝑥+ 𝑑 15𝑥𝑑𝑥+ 𝑑 4000𝑑𝑥 MC = 0.007 𝑑 𝑥3𝑑𝑥 −0.003 𝑑 𝑥2𝑑𝑥 +15 𝑑 𝑥𝑑𝑥+0 MC = 0.007 × 3 𝑥2−0.003 ×2𝑥+15 MC = 0.0021 𝑥2−0.006𝑥+15 We need to find MC when 𝑥=17 Putting 𝑥=17 MC = 0.021 172−0.006 17+15 MC = 6.069 – 0.102 + 15 MC = 20.967 Hence the Required Marginal cost is Rs. 20.967 when 𝒙=𝟏𝟕

Chapter 6 Class 12 Application of Derivatives

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.